Mohamed Mobarak ,Saleh Qaysi ,Mohamed Saad Ahmed ,Yasser F.Salama ,Ahmed Mohamed Abbass ,Mohamed Abd Elrahman ,Hamdy A.Abdel-Gawwad ,Moaaz K.Seliem

1 Physics Department,Faculty of Science,Beni-Suef University,Egypt

2 Geology and Geophysics Department,College of Science,King Saud University,11451 Riyadh,Saudi Arabia

3 Geology Department,Faculty of Science,Beni-Suef University,Egypt

4 Department of Building Materials,and Construction Chemistry,Institute of Civil Engineering,Technische Universit?t Berlin,Berlin,Germany

5 Structural Engineering Department,Faculty of Engineering,Mansoura University,Mansoura,Egypt

6 Raw Building Materials and Processing Technology Research Institute,Housing and Building National Research Center (HBRC),Cairo,Egypt

7 Faculty of Earth Science,Beni-Suef University,Egypt

Keywords:Coal Magnetic nanoparticles Cr(VI) adsorption Statistical models Thermodynamic parameters

ABSTRACT Herein,iron oxide/hydroxides deposits (gossans) were utilized,for the first time,in the fabrication of magnetite nanoparticles (MNPs) to load modified coal (MC).The as-synthesized MNPs@MC composite was characterized via different techniques and utilized for the Cr(VI) remediation.Experimental studies supported by theoretical treatment were applied to offer a new overview of the Cr(VI)adsorption geometry and mechanism at 25-45°C.Experimental results suggested that the Cr(VI)uptake was mainly governed by adsorption-reduction coupled mechanism.The Langmuir model fitted well the Cr(VI)adsorption data with maximum adsorption capacities extended from 115.24 to 129.63 mg·g-1.Theoretical calculations indicated that Cr(VI)ions were adsorbed on the MNPs@MC following the theory of the advanced monolayer statistical model.The number of ions removed per site ranged from 1.88 to 1.23 suggesting the involvement of vertical geometry and multi-ionic mechanism at all temperatures.The increment of the active sites density and the adsorption capacity at saturation with improving temperature reflected an endothermic process.Energetically,the Cr(VI) adsorption was controlled by physical forces as the adsorption energies were less than 40 kJ·mol-1.The calculated free enthalpy,entropy,and internal energy explained the spontaneous nature and the viability of Cr(VI) adsorption on the MNPs@MC adsorbent.These results offer a new approach in utilizing the iron-rich deposits as gossans in the preparation of magnetic and low-cost adsorbents for wastewater remediation.

1.Introduction

Contamination of water resources through the effluents of metal ions has become a severe worldwide challenge that definitely needs constructive solutions to avoid environmental and health hazards [1].Different industries as textile,paints,and pigments produce great amounts of chromium,which is a main problem due to the toxic characteristics associated with this metal ion[2,3].Generally,chromium can occur in two main forms (i.e.,hexavalent and trivalent) with dissimilar chemical and environmental characteristics [4].The hexavalent chromium Cr(VI) is more water soluble and toxic as compared to the Cr(III) form [5-7].Therefore,vomiting,lung cancer,liver damage,and nerve tissue injury are common human beings diseases results from the exposure to Cr(VI)-bearing water resources[6,7].Besides,the increment of Cr(VI) concentration in water can stop the growth of aquatic organisms [8,9].According to the US Environmental Protection Agency (EPA),0.1 and 0.05 mg·L-1are the maximum contaminant levels of Cr(VI) concentrations in domestic and drinking water,respectively [8,10].

Ion-exchange,chemical reduction,precipitation,and adsorption have been employed in removing chromium ions from water bodies [1,2,11].However,the majority of these remediation approaches have limited disadvantages as the low removal efficiency,extended uptake time,high cost,and probable formation of secondary contaminants [7-10].Treatment of Cr(VI)-rich water based on the adsorption method is highly recommended due to its simplicity,high efficiency,and low-cost [2,11].Numerous materials,includes agricultural wastes [12],CTAB-silica gelatin composite [13],treated zeolite [14],modified sunflower waste [15],modified rectorite [16],active carbon [17],spent clay [18],and organoclays [19] have been tested as Cr(VI) adsorbents.

Modeling the experimental data through the adsorption equilibrium models is significant to understand the physicochemical parameters that can control the removal process[20,21].The Langmuir and Freundlich models are regularly employed in fitting the experimental data as common classical models.The parameters of these models can offer evidences about the homogeneity or heterogeneity of the active sites as well as the uptake capacity without identifying the adsorbate geometry and the removal mechanism at the molecular scale [22-24].Thus,using the statistical physics concepts in fitting the experimental data is a reliable method to understand the adsorbent-adsorbate interface [23].Through the calculated steric and energetic parameters of the employed statistical models,the number of Cr(VI) ions adsorbed per active site (n),the active sites density of the MNPS@MC (magnetite nanoparticles to load modified coal) adsorbent (NM),the removed amount at saturation (Qsat),the Cr(VI) concentration at half-saturation(C1/2),and the adsorption energy(ΔE)can be calculated and interpreted [22-24].Consequently,interpretation of these parameters can offer new insights into the Cr(VI)ions geometry and the Cr(VI)-MNPs@MC interface mechanism.

Natural or synthetic materials rich in carbon were approved in water purification due to their high surface areas as well as the ability of these carbonaceous substances to interact with water pollutants through numerous binding forces [25].Furthermore,the interface between carbon-rich materials and nanoparticles has been demonstrated to be a confident approach in increasing the adsorption sites of the developed composites [26].In particular,the Fe-based nanoparticles were reported to be effective adsorbents for water pollutants due to their biocompatibility,great surface areas,and magnetic properties [27].However,Fe3O4nanoparticles have a high tendency to accumulate in solutions,and consequently,utilizing these magnetic nanomaterials without any support results in decreasing their removal performance and stability [28].Moreover,magnetic composites can be easily separated from the treated water by a magnet reflecting a simple and low-cost method for reusing these adsorbents numerous times.In previous studies,magnetic composites were prepared and employed as effective adsorbents in removing organic and inorganic water contaminants.For instance,magnetic polypyrrole/Fe3O4[10],CTA modified chitosan [9],and Fe3O4nanoparticles[24] were utilized in the removal of Cr(VI),methyl orange,and crystal violet,respectively.

Gossans(ferruginous deposits)are strongly weathered and oxidized rocks,which are usually related to the unprotected part of an ore deposit[29].The studied gossans deposit of Derhib area,South Eastern Desert,Egypt is composed mainly of quartz,hematite and goethite minerals [29].The current work aims to utilize iron oxides/hydroxides gossans as a new approach in the preparation of magnetite nanoparticles and their combination with modified coal for Cr(VI) adsorption.The physicochemical characteristics of the developed MNPs@MC adsorbent were investigatedviaXRD,TGA,DTG,FTIR,FESEM,and TEM techniques.In addition to the parameters of the classical models,the steric,energetic,and thermodynamic factors related to the advanced statistical physics models were applied to clarify and understand the Cr(VI)adsorption mechanism at the molecular level.The interpretation of these physicochemical parameters contribute to a better understanding for the orientation and adsorption mechanism of Cr(VI)on the MNPs@MC active sites.Overall,analyzing the experimental dataviathe statistical physics treatment is a confident approach for understanding the adsorption process at the micro-and macroscopic scales.

2.Materials and Methods

2.1.Materials

In this study,30 g of the prepared gossan powder with particlesize less than 100 μm was provided from the Applied Mineralogy Department,Beni-Suef,Egypt.In addition to using the dark brown gossan powder as Fe(III) source,the iron sulfate (FeSO4·7H2O,Loba Chemie,Mumbai,India)was utilized as Fe(II)source.A bituminous coal sample was supplied from Central Metallurgical Research and Development,Egypt.Hydrogen peroxide (H2O2),NH4OH solution,sodium hydroxide(NaOH),and hydrochloric acid(HCl)were delivered from Loba Chemie,Mumbai,India and used in the current study.

2.2.Preparation of modified coal (MC)

The utilized MC sample was prepared as follows [30]: A mass(10 g) of the natural coal sample was grounded and screened to size ＜100 μm.Hydrochloric acid(20%)and hydrofluoric(25%)acid were added to this sample and stirred at 40°C for 2 h to reduce its ash content.The activated coal sample was washed by distilled water and dried at 70 °C for 24 h.The dried coal sample was oxidized at 120 °C for 2 d to avoid the plastic result of the resinous materials.The oxidized coal was carbonized at 500 °C for 2 h to avoid a great lost in its original mass.Finally,the carbonized sample was modified by the addition of H2O2at 40°C for 30 min.After H2O2activation,the MC sample was washed with distilled water,dried at 70 °C,and used as a precursor in this study.

2.3.Synthesis of MNPs@MC adsorbent

The chemical precipitation method was used to prepare magnetite nanoparticles (MNPs) as follows [24]: Typically,1.25 g of FeSO4·7H2O and 2.5 g of the gossans powder were added to a clean glass beaker,which contains 3 g of MC and 25 ml of distilled water.This solid-liquid mixture was subjected to stirring for 30 min at room temperature(25°C).Then,15 ml of NH4OH(25%)as a precipitated agent was added slowly to this mixture.Under alkaline conditions,the MNPs with blacked color were formed after stirring for 120 min at 40 °C,as given in Eq.(1).

(*) refers to the Fe-oxide of the gossans.

The formed MNPs@MC was separated by a magnet,washed by distilled water/ethanol mixture,dried at 70 °C/16 h,and kept for characterization and adsorption experiments.Fig.1 displays the preparation method and the strong attraction between the MNPs@MC and an external magnet,which reflects the magnetic properties of the as-prepared product.

Fig.1.General and close-up views of gossans (a),and illustration of steps utilized for the preparation of MNPs@MC composite (b).

2.4.Sample characterization

X-ray diffraction patterns (XRD) of the MC and MNPs@MC samples were attained using a Philips APD 3720 diffractometer(Philips,USA) with Cu Kα radiation (40 kV,40 mA,and λ=0.154 nm)at 2θ=5.02°-49.98°with a speed rate of 5(°)·min-1.The functional groups of the investigated samples (i.e.,MC and MNPs@MC) were identified at room temperature using Fourier transform infrared spectrometer (FTIR,Bruker 2000,Germany) in the range of 400-4000 cm-1.Thermogravimetric(TGA)and derivative thermogravimetry(DTG)analyses were used to determine the weight losses percentages attributed to the change in the studied samples.Both of the TGA and DTG studies were achieved by a DT-50 thermal analyzer (Schimadzu,Japan).The morphological properties of MC and MNPs@MC samples were detected using a Field emission scanning electron microscope (FESEM,Sigma 500,ZEISS,Germany) and transmission electron microscope (TEM,JEM-1400,JEOL,Japan).

2.5.Cr(VI) equilibrium studies and modeling analysis

Firstly,a standard solution(1000 mg·L-1)of Cr(VI)was prepared and diluted by adding deionized water to obtain the required concentrations (i.e.,10-100 mg·L-1) of this adsorbate.The Cr(VI)uptake experiments were performed at pH 3.0 and temperatures of 25,35,and 45 °C.The additional conditions related to the Cr(VI) isotherms experiments were: 25 mg of the MNPs@MC mass and 50 ml of each chromate concentration.The chromate-MNPs@MC mixtures were stirred at 120 r·min-1for 240 min(equilibrium time)using an orbital shaker.The chromate solutions were separated by centrifuging and then the DX-120 ion chromatograph(Dionex,USA) was used to determine the Cr(VI) concentration in solutions.The removed quantities of Cr(VI) at equilibrium(qe,mg·g-1) were calculated using the next equation.

in whichC0(mg·L-1)is the initial Cr(VI)concentration,Ce(mg·L-1)is the chromate ion concentration at equilibrium,V(L) is the volume of chromate solution,andm(g) is the mass of the MNPs@MC adsorbent.

All Cr(VI) adsorption experiments were conducted three times and thus,the expressed results in this article correspond to the average values—the comparative standard deviation of the measurements ≤4.0%.

2.6.Classical and advanced modeling for Cr(VI) adsorption on MNPs@MC

In this paper,the non-linear methods of the Langmuir [31]and Freundlich [32] models were used in fitting the Cr(VI)adsorption data at different solution temperatures.In addition,the determination coefficient (R2) and Chi-square (χ2) values were used to find the best-fitted model,see Table 1.Besides,three statistical physics models (i.e.,monolayer,double-layer,and multilayer) were also employed to analyze the Cr(VI)adsorption process.The mathematical methods used to measure the adsorbed amounts related to these adsorption models are described in Table 1.TheR2and the root mean square error(RMSE) values (Table 1) were used to determine the acceptable statistical adsorption model.The concepts of the three statistical physics adsorption models were presented below[22,23]:

Table 1 Traditional and advanced statistical physics models used for analyzing Cr(VI) adsorption on the MNPs@MC composite

· Monolayer model with one energy(Model 1).Cr(VI)adsorption on MNPs@MC forms a sole layer ruled by one adsorption energy(ΔE) for all active sites.

· Double-layer model with two energies (Model 2): Cr(VI)adsorption is theorized to occur through the formation of two chromate layers with two dissimilar adsorption energies (ΔE1and ΔE2).It is important to clarify that the ΔE1defines the MNPs@MC-Cr(VI) interaction,while the ΔE2refers to the Cr(VI)-Cr(VI) interface.

· Multilayer model (Model 3): Cr(VI) adsorption is characterized by a specified number of the chromate layers that are controlled by different adsorption energies (i.e.,ΔE1and ΔE2).

3.Results and Discussion

3.1.Characterization of the MNPs@MC composite

The XRD diffraction patterns of the MC and the developed MNPs@MC composite are shown in Fig.2.The MC sample was mainly characterized by an amorphous outline with the presence of two diffraction peaks at 2θ=28.54° and 43.67°,which correspond to the graphite mineral [30].Concerning the XRD results of the MNPs@MC,the peaks observed at 2θ=30.51° (220),35.76°(311),and 43.61° (400) reflected the loading of MC sample by the magnetite nanoparticles [33].The decrease of intensity or the disappearance of the peaks related to carbon reflected the interface between the MC sample and the fabricated MNPs.In addition,some peaks related to goethite and hematite as Fe-bearing minerals were detected,and therefore,Fe2O3of gossans was not totally involved in the formation of MNPs.

Fig.2.XRD patterns of the MC and the MNPs@MC composite.

FTIR spectrum of the MNPs@MC composite shows different transmittance bands at 3410.60,2912.13,2843.17,1724.53,1571.06,and 1090.71 cm-1,see Fig.3(a).These transmittance peaks are related to the stretching vibration of the —OH group inside binding water molecules and the cellulosic compounds (at 3410.6 cm-1) [34],the asymmetric and symmetric stretching vibration of C—H (2912-2840 cm-1),and the C=C inside the aromatic ring (1566-1623 cm-1) [35].The detected band at 1724.53 cm-1could be assigned to the stretching of C=O group[30].The observed two bands at 1571.06,and 1090.71 cm-1could be attributed to the NH and the stretching Si—O group,respectively[30].The noticeable transmittance bands at 605.65 and 461.24 cm-1can be assigned to the Fe—O vibrational modes,while the band detected at nearly 564 cm-1characterizes the Fe—O stretch vibrations of Fe3O4nanoparticles [24].Thus,the detection of these bands reinforced the modification of MC sample by MNPs producing a magnetic multifunctional MNPs@MC composite.Fig.3(b)reports the TG/DTG curves of the as-prepared MNPs@MC.Three main stages were observed at different temperatures inside the TGA/DTG-curve of the MNPs@MC composite.The first and second stages suggested the removal of free water or moisture (6.27% at 75 °C) and the oxidation of organic carbon (2.17% at 300 °C),respectively.The final stage detected at a temperature range of 600-915°C was related to the complete combustion of amorphous carbon and the oxidation of iron nanoparticles (65.02%) [36],reflecting the thermal stability of MNPs@MC up to～500 °C.

Fig.3.FTIR spectrum (a) and TGA/DTG curves (b) of the MNPs@MC composite.

FESEM images (Fig.4(a)) show the existence of disconnected graphite sheets with numerous open holes,which supporting the interface between H2O2and the coal sample.The created cavities and pores can facilitate the prepared MNPs to be inserted in the porous structure of the MC sample.Therefore,the spherical Fe3O4nanoparticles with particle size below 50 nm can fill the holes/or pits of the MC or coated its surface.(Fig.4(b)-(d)).Also,FESEM results indicated that the MC as a support material can positively reduce the degree of accumulation related to the magnetite properties of the as-synthesized magnetite nanoparticles [36].Overall,impregnation of MNPs with the MC can increase significantly the performance of the developed MNPs@MC composite for the removal of water contaminates [24].

Fig.4.FESEM images of MC (a) and MNPs@MC (b,c,and d).

TEM photographs (Fig.5(a)) show smooth sheets of the MC sample free from black spherical lumps.Moreover,the MC sheets presented a width ranging from 110 to 150 nm and a length of 175-195 nm.TEM images(Fig.5(b))clearly reflected the scattering of MNPs nanoparticles onto the MC surface,which was in good agreement with the obtained FESEM results.

Fig.5.TEM images of MC (a) and MNPs@MC (b).

3.2.Effect of initial pH on Cr(VI) adsorption onto MNPs@MC

The pH value is a main parameter affecting the adsorption system as it can govern the MNPs@MC surface properties and the ionization of the chromium in the aqueous medium [37].Numerous pH values ranged from 3.0 to 10.0 were conducted to find the optimum performance for the tested adsorbent in removing the Cr(VI)ions.The pH influence was determined using 0.025 g of MNPs@MC,50 mg·L-1of Cr(VI)concentrations,4 h of shaking time,and 25°C of solution temperature,and the results are described in Fig.6(a).Obviously,the maximum removal percentage of Cr(VI) was observed at pH 3.0 (91.2%),and this percentage decreased with the increment of pH value.At low pH values (i.e.,pH 3.0 and 4.0)the MNPs@MC surface was positively charged due to the protonation of the MNPs@MC functional groups(e.g.,—,and Fe—).On the other hand,at pH 3.0,the main form of chromate is HCrO4-,which interacted distinctly with the positively charged MNPs@MC active sites.Furthermore,the presence of —NH2(i.e.,electrondonor functional group) on the MNPs@MC surface contributed to reduce the Cr(VI) to Cr(III) and therefore,the trivalent chromium can be removed by the surface functional groups (i.e.the —OH groups) of the MNPs@MC by addition [21].Simultaneously,a substitution reaction between the Cr3+and the positively charged MNPs@MC surface (i.e.,—and —) at pH 3.0 enhanced the Cr(VI)removal percentage.At high pH values,both of the hydroxyl ions and the negativity active sites increased,which resulted in decreasing the uptake percentages of Cr(VI) due to the repulsion force.Accordingly,the pH 3.0 was selected to carry out all and Cr(VI) adsorption experiments.In addition,pH of the point of zero charge (pHPZC) of the as-synthesized MNPs@MC adsorbent was resulted to be 5.7 and,therefore,this composite was effective for the removal of chromate ions at solution pH below 6.0,see Fig.6(b).

Fig.6.Effects of pH on the Cr(VI) adsorption (a) and pHPZC of MNPs@MC adsorbent (b).

3.3.Classical isotherm models

Fig.7 shows the modeling results of the Cr(VI) adsorption on the MNPs@MC surface using the Langmuir and Freundlich equations,while the adaptable factors of these simple models are offered in Table 2.Based on the attainedR2and χ2values at 25,35,and 45 °C,the Langmuir model was the best in fitting the Cr(VI) adsorption data as compared to the Freundlich equation at these solution temperatures.Therefore,the adsorption of Cr(VI)was related to similar active sites of the tested adsorbent and the interface between chromate ions and MNPs@MC generated a single layer of Cr(VI).The maximum adsorption capacities (qmax) of this adsorbent were 115.24,125.32,and 129.63 mg·g-1at 25,35,and 45 °C,respectively,see Table 2.The increase ofqmaxvalues with improving temperature reflected an endothermic process[21-24].The MNPs@MC adsorbent presented a great value ofqmax(115.24 mg·g-1)as compared to different materials.For example,theqmaxvalues of Cr(VI) were 15.2,4.3,24.1,21.0,10.4,and 67.05 mg·g-1for carbon slurry,Akadama clay,activated clay,modified rectorite,treated rice husks,and CTAB/H2O2-clay,respectively [38].Consequently,the as-synthesized MNPs@MC can be suggested as a reliable and low-cost composite for decontamination of Cr(VI)-bearing solutions.Furthermore,the increment ofKFvalues from 59.11 to 90.71 ((mg·g-1)(mg·L-1)-1/n) with increasing temperature also suggested the endothermic performance of this adsorption process[23,24].The determined 1/nvalues were below unity signifying a promising Cr(VI)-MNPs@MC interaction even at low concentrations of chromate ions [24].

Table 2 Parameters of isotherms models for Cr(VI) uptake by MNPs@MC

Fig.7.The Langmuir and Freundlich models at 25 °C (a),35 °C (b),45 °C (c) and the monolayer adsorption model at different temperatures (d) for the Cr(VI) uptake by MNPs@MC composite.

3.4.Statistical physics modeling of Cr(VI) adsorption on MNPs@MC

Based on the highestR2and the lowest RMSE values,the monolayer model with one energy(Model 1)was preferred for fitting the Cr(VI) adsorption results at all temperatures,see Fig.7.Consequently,Model 1 was used to understand the steric(i.e.,n,NM,Qsat)and energetic (ΔE) parameters involved in the removal process.

3.5.Interpretation of steric parameters

The stericnparameter can be utilized to describe the degree of chromate ions aggregation and their geometric situations on the MNPs@MC surface[20].According to thenparameter,three situations can be used to define the position and mechanism of the removed Cr(VI) ions by the MNPs@MC composite [22,23].The 1st state(n＜0.5):Cr(VI)ions can be adsorbed by two or more adsorption sites of the MNPs@MC composite donating a parallel orientation,which corresponds to and multi-docking removal mechanism,the 2nd state(0.5 ＜n＜1):Cr(VI)ions can be captured at the same time by parallel and non-parallel orientations displaying a mixed adsorption geometry,and the 3rd state(n≥1):This final state suggests that the functional group of MNPs@MC can accept one or more Cr(VI)ions,thus suggesting a non-parallel orientation equivalent to a multi-molecular mechanism.Fig.8 displays the calculatednvalues as a function of adsorption temperature and the calculated values were presented in Table 3.Thenvalues ranged between 1.88 and 1.23 signifying the involvement of vertical geometry (non-parallel orientation) and multi-ionic mechanism at 25,35,and 45 °C.This result suggested that numerous Cr(VI)ions were removed by one active adsorption site of the MNPs@MC adsorbent forming a vertical geometry.Also,increasing the temperature has no a clear effect in altering the position and mechanism as thenvalues were superior to unity at all temperatures.

Table 3 Steric and energetic parameters of the monolayer adsorption model for the Cr(VI)removal by MNPs@MC composite

Fig.8.Evolutions of n, NM, Qsat,and ΔE as function of temperature for Cr(VI) adsorption.

The style of the stericNMparameter attributed to the uptake of Cr(VI)by MNPs@MC composite is presented in Fig.9.TheNMvalue increased from 55.66 to 102.65 mg·g-1inside the temperature range of 25-45°C,see Table 3.Enhancing this parameter with temperature could be associated to the involvement of further MNPs@MC active sites in the removal of chromate ions [22,23].Additionally,the determinedNMconfirmed the endothermic interface between the Cr(VI) and the MNPs@MC active sites.As theNMincreased with the adsorption temperature,the correspondingndecreased (i.e.,opposite style characterized the two steric parameters).

Fig.9.Evolutions of entropy,Gibs free energy and internal energy as function of temperature for Cr(VI) adsorption.

The adsorption capacity(Qsat=nNM)at saturation is an important factor to recognize the performance of the MNPs@MC adsorbent for sequestrating the Cr(VI) ions.For Model 1 (monolayer with the same energy),It can be standard thatQsatincreased from 104.98 to 126.26 mg·g-1with rising temperature from 25 to 45°C,see Fig.9 and Table 3.This result suggested that Cr(VI) adsorption was endothermic (i.e.,the removal of chromate was preferred at high solution temperatures).Both of theQsatandNMparameters increased with temperature and thus,the density of MNPs@MC receptor sites was suggested to be the main parameter that can control the uptake performance of this adsorbent.

3.6.Interpretation of energetic parameters

Model 1 proposes the occurrence of one adsorption energy(ΔE)at each temperature that can be complicated in the Cr(VI)removal and the ΔEwas determined as follows [23]:

wherec1/2signifies to the concentrations at half-saturation andcsis the Cr(VI) solubility.

Fig.9 and Table 3 display the values of adsorption energies related to the Cr(VI) uptake at the applied solution temperatures.Clearly,the ΔEoffered positive values,which suggested the endothermic nature of the adsorption system.Overall,the adsorption energies were ＜40 kJ·mol-1suggesting that physical interaction (i.e.,electrostatic interactions and van der Waals forces)could be involved in the removal of chromate ions.Energetically,the ΔEtrend was similar to that of theQsatas a function of temperature.Therefore,the chromate adsorption on MNPs@MC was mainly governed by the steric (NM) and the energetic (ΔE)parameters.

3.7.Thermodynamic functions

Calculation of entropy,free enthalpy,and internal energy as thermodynamic parameters is significant in the macroscopic explanation related to the interaction between the Cr(VI) and MNPs@MC composite.

3.7.1.Entropy

The similarity degree (i.e.,order and/or disorder) of the captured Cr(VI)ions by the MNPs@MC surface can be assessed through calculating the entropy of the adsorption system.Using the grand potential (J) and the total grand canonical partition function (Zgc),the entropy was determined by [39]:

where β is defined as 1/kBT(wherekBis the Boltzmann constant andTis the absolute temperature).

Concerning the monolayer layer model with one energy(Model 1),entropy was calculated as reported below [40].

The difference of the configurational entropy as a function of the chromate concentration is offered in Fig.9(a).Before the half-saturation concentration,it can be noticed that the entropy(the disorder degree) enhanced obviously with increasing the Cr(VI) concentration till a highest value.Normally,this random case increased at the start of Cr(VI)uptake process due to the existence of more active sites on the MNPs@MC composite surface available to sequestrate the chromate ions.After the half-saturation,a decrease in the entropy parameter was observed reflecting the foundation of an order state.Increasing this order state was mainly attributed to the decrease of the accessible active adsorption sites on the MNPs@MC adsorbent [39].

3.7.2.Free enthalpy

Calculation of the free enthalpy is significant in defining the type of the Cr(VI) adsorption system (i.e.,spontaneous or not).Using the Model 1,the free Gibbs enthalpy was calculated as follows [40].

in which μ is the chemical potential of the adsorbed chromate,ztris the translational partition per unit volume.

The behavior of the free enthalpy versus the Cr(VI) concentration is presented in Fig.9(b).The enthalpy attained a maximum value at the beginning of the removal process due to the strong interaction between Cr(VI) ions and the MNPs@MC adsorbent[39].It can be realized that the Cr(VI) adsorption process is spontaneous because of the negative value of the free enthalpy.Furthermore,the feasibility of the chromate adsorption system enhanced with increasing temperature due to the increment of the free enthalpy.

3.7.3.Internal energy

The internal energy can be calculated using the following formula [40].

For Model 1,the next expression was utilized in calculating the internal energy of the adsorption process [40].

Determining the values of internal energy is an important factor in understanding the spontaneity of the chromate adsorption onto the MNPs@MC surface.Fig.9(c) shows the development of the internal energy versus the chromate concentration.The negative values of the internal energy suggested that the Cr(VI) adsorption occurred spontaneously.

4.Conclusions

Gossans as iron oxide/hydroxides deposits were utilized in the synthesis of magnetite nanoparticles to load modified coal producing a magnetic MNPs@MC composite.This new material was employed as an effective adsorbent for Cr(VI) from solutions.The experimental results were adjusted to classical and statistical physics models at different solution temperatures.The Langmuir and the advanced monolayer models fitted well the adsorption data.The steric,energetic,and thermodynamic parameters attributed to the monolayer model were attained and deeply discussed.The vertical position and multi-ionic mechanism were involved in the Cr(VI)-MNPs@MC interaction at all adsorption temperatures.The removal of Cr(VI)was endothermic and directed by physical forces with adsorption energies below 40 kJ·mol-1.Thermodynamic parameters reflected the spontaneous nature and the viability of the adsorption process.These results offered a new approach in using Fe-rich deposits as gossans in the preparation of effective and low-cost magnetic composites.Also,the theoretical treatment offered novel insights into the adsorption performance and mechanism for removing Cr(VI) using the MNPs@MC adsorbent.

Data Availability

The authors do not have permission to share data.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by Researchers Supporting Project number (RSP2023R455),King Saud University,Riyadh,Saudi Arabia.